ارائه یک مدل یک بعدی برای برآورد توزیع سرعت درکانال روباز کم‌عرض

نویسندگان
حسین بنکداری 1
نگین بینش 2
1 دانشگاه رازی کرمانشاه
2 دانشگاه تهران
چکیده
برآورد توزیع سرعت به عنوان یک پارامتر کلیدی در تخمین دیگر پارامتر‌های هیدرولیکی جریان نظیر دبی و تنش برشی از اهمیت زیادی برخوردار است؛ و در دهه‌های اخیر، برآورد پروفیل توزیع سرعت جریان در کانالهای کم‌عرض با نسبت عرض به عمق کمتر از 5، توجه بسیاری از محققین را به خود معطوف داشته است. در این مقاله یک مدل تحلیلی برای برآورد توزیع سرعت جریان آشفته و کاملا توسعه یافته، بر مبنای میانگین گیری رینولدز معادلات ناویر استوکس (RANS) و یک توزیع لزجت گردابی ارائه شده است. مدل پیشنهادی قابلیت کاربرد در هر دو دسته کانالهای عریض و کم‌عرض را دارد. این مدل با داده‌های اندازه‌گیری شده در کانال‌های آزمایشگاهی مستطیلی و نیز داده‌های حاصل از یک سایت واقعی کانال فاضلاب مقایسه و معتبرسازی شده است. به دلیل وابستگی معادله توزیع سرعت پیشنهادی به پارامتر کولز، تأثیر این پارامتر بر میزان دقت در توصیف پروفیل سرعت و پیش بینی محل وقوع سرعت ماکزیمم نیز مورد مطالعه قرار گرفته است. در مطالعه حاضر، پارامتر کولز از طریق برازش به دست آمده و مقادیری که به ازای آن، مدل پیشنهادی کمترین میزان خطا را در برآورد پروفیل سرعت ارائه می‌دهد، پیشنهاد گردیده است. نتایج نشان می‌دهد که پروفیل‌های سرعت به دست آمده از مدل پیشنهادی مطابقت بالایی با داده‌های اندازه‌گیری شده داشته و گرادیان منفی سرعت در نزدیکی سطح آزاد آب را به خوبی نشان می‌دهد. مقدار پارامتر کولز برای کانال فاضلاب کمتر از مقدار این پارامتر برای کانال‌های آزمایشگاهی به دست آمد.

کلیدواژه‌ها

عنوان مقاله English

Introducing one-dimensional model to estimate velocity distribution in narrow open-channels

نویسندگان English

Hossein Bonakdari 1
Negin Binesh 2
چکیده English

In open channels, the distribution of velocity, shear stress and other related quantities such as the diffusion and dispersion coefficients and thus all transport processes are three-dimensional, according to the three-dimensional convection and diffusion principles. Determining the velocity distribution- as a key parameter for estimating other hydraulic parameters- has always been the subject of attention. Velocity distribution in the inner region of the flow (y0.2D). The log-Wake law is of the most accepted laws for velocity distribution in wide open channels, this law modifies the logarithmic law by adding a Wake function; but in case of narrow open channels, the log-Wake law deviates from the measured data near the free surface. Because the profile by the log-Wake law depicts the velocity which increases with the increase of distance from the bed monotonically and is not able to show the velocity negative gradient near the free surface which happens in narrow open channels. In narrow open channels, the three dimensional structure of the flow and the transport momentum from the side walls to the central zone due to strong secondary currents, causes the maximum velocity to occur below the water surface which is called velocity-dip phenomenon. The velocity dip phenomenon was first reported more than a century ago. Since that time, numerous investigations have been conducted by many researchers in order to propose new models to be able to not only describe the dip phenomenon and negative gradient of velocity near the free surface, but also to predict the position of the maximum velocity accurately and fit the experimental data throughout the whole flow depth.
This paper introduces an analytical model based on Reynolds Averaged Navier Stokes (RANS) equations and an eddy viscosity distribution, to estimate velocity distribution in turbulent fully developed flows. The proposed model is suitable for both narrow and wide open channels, and is capable of predicting the dip phenomenon. The results by the model verified with data measured in several rectangular lab channels and data collected from an actual sewer channel. Since the proposed equation for velocity distribution is dependent of Coles Wake parameter (Π), the effect of this parameter on level of accuracy and description of velocity profile as well as prediction of dip phenomenon and location of maximum velocity has been studied. Many researchers proposed different values for Coles parameter, and it seems there is no universal constant value for this parameter. In this study, the value of Coles parameter was proposed by fitting the data from different channels, based on the least error calculated in predicting the velocity profiles by the proposed model. The results show that the profiles by the model agree well with experimental data and predict the velocity-dip phenomenon; also the model provides little errors compared to measured data in the channels, which is representative of high level of accuracy in defining velocity distribution profile of the flow. The value of Coles parameter estimated for channel-sewer was less than that for lab channels.

کلیدواژه‌ها English

Velocity distribution
eddy viscosity
Coles Wake parameter
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مهندسی عمران مدرس
دوره 16، شماره 5
آذر و دی 1395
صفحه 33-43